spyrit.misc.walsh_hadamard.iwalsh_S

spyrit.misc.walsh_hadamard.iwalsh_S(s, T=None)[source]

Return the inverse Walsh S-transform of the signal x

Args:

x (np.ndarray): signals of shape (*,n), where n+1 must be a power of two.

H (np.ndarray, optional): Inverse S-matrix of order n.

Returns:

np.ndarray: S-transformed signal of shape (*,n).

Examples:

Example 1: Inverse Walsh-ordered S-transform of a signal of length 7

>>> import spyrit.misc.walsh_hadamard as wh
>>> s = np.array([12, 9, 9, 16, 4, 5, 9])
>>> x = wh.iwalsh_S(s)
>>> print(x)
[ 1.  3.  0. -1.  7.  5.  1.]

Example 2: Walsh-ordered S-transform of two signals of length 7

>>> s = np.array([[12, 9, 9, 16, 4, 5, 9],[12, 4, 8, 12, 6, 6, 8]])
>>> x = wh.iwalsh_S(s)
>>> print(x)
[[ 1.  3.  0. -1.  7.  5.  1.]
 [ 2.  1. -1.  0.  4.  5.  3.]]

Example 3: Foroward and inverse S-transform of two signals of length 4095

>>> import spyrit.misc.walsh_hadamard as wh
>>> import numpy as np
>>> x = np.random.rand(2,4095)
>>> s = wh.walsh_S(x)
>>> y = wh.iwalsh_S(s)
>>> err = np.linalg.norm(1-y/x)
>>> print(f'Error: {err}')
Error: ...e-...
>>> print(err < 1e-5)
True